This book comprises a collection of 125 problems and snapshots from discrete probability. The problems are selected on the basis of their historical interest whereas the snapshots provide quick overviews of topics in probability such as Markov chains, Poisson processes, random walks, patterns in random sequences, cover times, and embedding procedures. This book will appeal to all those who enjoy problems with probabilistic flavour. The authors presuppose a basic exposure to discrete mathematics and elementary probability. Students will find this a stimulating companion to their courses in probability. More advanced researchers will appreciate the original style of the problems, some of which may even inspire new areas for research.